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H∞ fault detection filter design for networked control systems in the continuous-time domain

H Fault Detection Filter Design for Networked Control Systems in the Continuous-time Domain
H
∞
Fault Detection Filter Design for Networked Control Systems in
the Continuous-time Domain
Liu Yunxia *, Wang Huijing , and Liu Junyao
* Corresponding author: Tel.: (86)755-89226352; E-mail: yunxialiu@126.com
Computer College
Shenzhen Institute of Information Technology
Shenzhen, Guangdong Province, P.R. China
ABSTRACT
This paper deals with the problem of fault detection filter design for a class of networked control systems. Under
the assumptions of network-induced time delay being unknown but bounded, packet dropouts and packets out of
sequence being unavoidable, a system model for networked control system is firstly introduced in the
continuous-time domain. Then an observer-based H fault detection is formulated and, by applying the
Lyapunov-Krasovskii functional approach, a delay-dependent sufficient condition on the existence of the H fault
detection filter (FDF) is derived in terms of matrix inequality. Furthermore, an algorithm is proposed to get a
feasible solution to the H fault detection filter gain matrices in terms of linear matrix inequalities (LMIs) using a
cone complementary technology. A simulation example is given to demonstrate the effectiveness of the proposed
method.
1. INTRODUCTION
Over the past decades, fault detection and isolation (FDI) was an active field of research due to an increasing
demand for higher performance, as well as higher safety and reliability standards [1~3]. Furthermore, with the rapid
development and wide application of communication networks, the FDI problem for networked control systems
(NCSs) has also received much attention recently [4~7]. It is noted that models of NCSs in the above references were
discrete-time system and, therefore, the discretization were needed for NCSs with continuous-time dynamic processes,
such that the inter-sampling behaviors were not taken into account. When the network-induced delay is unknown but
bounded, the continuous-time system model proposed in references [8, 9] are more reasonable. To authors’ best
knowledge, however, Zhong and Han [10] studied the problem of fault detection filter design in the continuous-time
domain, which is on the assumption of network induced delay (controller-to-actuator) being known. Due to time-delays
frequently encountered in practical control systems, and packet dropouts and packets out of sequence is also
unavoidable, the problem of fault detection for NCSs is still open and remains challenging, which is the main
motivation of this study.
In this paper, we will design the fault detection filter for a class of networked control systems. Under the
assumptions of network-induced time delay being unknown but bounded, packet dropouts and packets out of sequence
being unavoidable, the FDF design will be investigated in the continuous-time domain.
2. PROBLEM FORMULATION
Consider an NCS with plant, actuators, sensors, a controller and an FDF, which is depicted in Figure 1. The plant is
a continuous-time linear time-invariant (LTI) process, which can be expressed by

H Fault Detection Filter Design for Networked Control Systems in the Continuous-time Domain
H
∞
Fault Detection Filter Design for Networked Control Systems in
the Continuous-time Domain
Liu Yunxia *, Wang Huijing , and Liu Junyao
* Corresponding author: Tel.: (86)755-89226352; E-mail: yunxialiu@126.com
Computer College
Shenzhen Institute of Information Technology
Shenzhen, Guangdong Province, P.R. China
ABSTRACT
This paper deals with the problem of fault detection filter design for a class of networked control systems. Under
the assumptions of network-induced time delay being unknown but bounded, packet dropouts and packets out of
sequence being unavoidable, a system model for networked control system is firstly introduced in the
continuous-time domain. Then an observer-based H fault detection is formulated and, by applying the
Lyapunov-Krasovskii functional approach, a delay-dependent sufficient condition on the existence of the H fault
detection filter (FDF) is derived in terms of matrix inequality. Furthermore, an algorithm is proposed to get a
feasible solution to the H fault detection filter gain matrices in terms of linear matrix inequalities (LMIs) using a
cone complementary technology. A simulation example is given to demonstrate the effectiveness of the proposed
method.
1. INTRODUCTION
Over the past decades, fault detection and isolation (FDI) was an active field of research due to an increasing
demand for higher performance, as well as higher safety and reliability standards [1~3]. Furthermore, with the rapid
development and wide application of communication networks, the FDI problem for networked control systems
(NCSs) has also received much attention recently [4~7]. It is noted that models of NCSs in the above references were
discrete-time system and, therefore, the discretization were needed for NCSs with continuous-time dynamic processes,
such that the inter-sampling behaviors were not taken into account. When the network-induced delay is unknown but
bounded, the continuous-time system model proposed in references [8, 9] are more reasonable. To authors’ best
knowledge, however, Zhong and Han [10] studied the problem of fault detection filter design in the continuous-time
domain, which is on the assumption of network induced delay (controller-to-actuator) being known. Due to time-delays
frequently encountered in practical control systems, and packet dropouts and packets out of sequence is also
unavoidable, the problem of fault detection for NCSs is still open and remains challenging, which is the main
motivation of this study.
In this paper, we will design the fault detection filter for a class of networked control systems. Under the
assumptions of network-induced time delay being unknown but bounded, packet dropouts and packets out of sequence
being unavoidable, the FDF design will be investigated in the continuous-time domain.
2. PROBLEM FORMULATION
Consider an NCS with plant, actuators, sensors, a controller and an FDF, which is depicted in Figure 1. The plant is
a continuous-time linear time-invariant (LTI) process, which can be expressed by